Controller design and value function approximation for nonlinear dynamical systems

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21230%2F16%3A00303440" target="_blank" >RIV/68407700:21230/16:00303440 - isvavai.cz</a>

Výsledek na webu

<a href="http://dx.doi.org/10.1016/j.automatica.2016.01.022" target="_blank" >http://dx.doi.org/10.1016/j.automatica.2016.01.022</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.automatica.2016.01.022" target="_blank" >10.1016/j.automatica.2016.01.022</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Controller design and value function approximation for nonlinear dynamical systems

Popis výsledku v původním jazyce

This work considers the infinite-time discounted optimal control problem for continuous time input-affine polynomial dynamical systems subject to polynomial state and box input constraints. We propose a sequence of sum-of-squares (SOS) approximations of this problem obtained by first lifting the original problem into the space of measures with continuous densities and then restricting these densities to polynomials. These approximations are tightenings, rather than relaxations, of the original problem and provide a sequence of rational controllers with value functions associated to these controllers converging (under some technical assumptions) to the value function of the original problem. In addition, we describe a method to obtain polynomial approximations from above and from below to the value function of the extracted rational controllers, and a method to obtain approximations from below to the optimal value function of the original problem, thereby obtaining a sequence of asymptotically optimal rational controllers with explicit estimates of suboptimality. Numerical examples demonstrate the approach.

Název v anglickém jazyce

Controller design and value function approximation for nonlinear dynamical systems

Popis výsledku anglicky

This work considers the infinite-time discounted optimal control problem for continuous time input-affine polynomial dynamical systems subject to polynomial state and box input constraints. We propose a sequence of sum-of-squares (SOS) approximations of this problem obtained by first lifting the original problem into the space of measures with continuous densities and then restricting these densities to polynomials. These approximations are tightenings, rather than relaxations, of the original problem and provide a sequence of rational controllers with value functions associated to these controllers converging (under some technical assumptions) to the value function of the original problem. In addition, we describe a method to obtain polynomial approximations from above and from below to the value function of the extracted rational controllers, and a method to obtain approximations from below to the optimal value function of the original problem, thereby obtaining a sequence of asymptotically optimal rational controllers with explicit estimates of suboptimality. Numerical examples demonstrate the approach.

Druh

J_x - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)

CEP obor

BC - Teorie a systémy řízení

OECD FORD obor

—

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2016

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Automatica

ISSN

0005-1098

e-ISSN

—

Svazek periodika

67

Číslo periodika v rámci svazku

May

Stát vydavatele periodika

GB - Spojené království Velké Británie a Severního Irska

Počet stran výsledku

13

Strana od-do

54-66

Kód UT WoS článku

000373540300006

EID výsledku v databázi Scopus

2-s2.0-84960432002